What is the integral from 6 to 100 of 0.5x^{-1.5} ?

The integral from 6 to 100 of 0.5x^{-1.5} is 0.30824…

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integral from 6 to 100 of 0.5x^{-1.5}

\int_{6}^{100} 0.5 x^{- 1.5} d x

0.30824 \dots

Solution steps

\int_{6}^{100} 0.5 x^{- 1.5} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 0.5 \cdot \int_{6}^{100} x^{- 1.5} d x

Apply the Power Rule

: [- \frac{2}{x}]_{6}^{100}

= 0.5 [- \frac{2}{x}]_{6}^{100}

Compute the boundaries:

- \frac{1}{5} + \frac{2}{3}

= 0.5 (- \frac{1}{5} + \frac{2}{3})

Simplify

= 0.30824 \dots

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What is the integral from 6 to 100 of 0.5x^{-1.5} ?
The integral from 6 to 100 of 0.5x^{-1.5} is 0.30824…